It is permissible for a fasting person to cool himself down, and there is no objection to it, for the Messenger sallAllaahu ‘alayhi wa sallam used to pour water over his head due to heat or thirst and he was fasting [1], and Ibn ‘Umar, may Allaah be pleased with them, used to wet his garment when he was fasting in order to alleviate the excessive heat and thirst. And the wetness has no effect, because in such cases water does not reach the stomach.

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[1] Reported by Abu Dawud in the Book of Fasting, in the Chapter: The Fasting Person May Pour Water Over Himself Due to Thirst (2365).